Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.
Mathematical Operations Reasoning QuestionsSandip Kar
Solved examples of verbal reasoning questions and answers on “Mathematical Operations” with explanation with detailed answer description, explanation. Suitable for various competitive exams like Bank PO, IBPS, LIC, Railways and SBI Clerk.
Mathematical Operations Reasoning QuestionsSandip Kar
Solved examples of verbal reasoning questions and answers on “Mathematical Operations” with explanation with detailed answer description, explanation. Suitable for various competitive exams like Bank PO, IBPS, LIC, Railways and SBI Clerk.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
1. Subtract 1
2 mark for improper fraction or incorrect rounding.
Question marks: 5, 8, 14, 6, 11, 10, 16, 15, 8, 7
1. (a) Evaluate y2
x−1
+ 2x when y = 2 and x = 4. (2 marks)
(22
× 4−1
) + 2 × 4 = 9
1 mark for working, 1 mark for answer.
(b) Simplify (x
3/2
÷ x3
)4
. (3 marks)
(x
3/2
÷ x3
)4
= (x
3/2−3
)4
= (x
− 3/2
)4
= x−6
1 mark for working, 2 marks for solution.
2. (a) What is the equation of the line passing through the points (1, 7)
and (−1.5, −3)? (4 marks)
m = 7−(−3)
1−(−1.5) = 4 1 mark
7 = 4 × 1 + c 1 mark
c = 3 1 mark
y = 4x + 3 1 mark
(b) Solve the simultaneous equations (4 marks)
x + y = −2
12x − 3y = −9
3 × eqn1: 3x + 3y = −6 2 marks for cancelling or substitution
eqn2 + 3 × eqn1: 15x = −15
x = −1 1 mark
−1 + y = −2
y = −1 1 mark
3. (a) Differentiate y = −3x2
+ 2x + 1. (2 marks)
dy
dx = −6x + 2
(b) What are the x and y co-ordinates of the stationary point of the
graph
y = −3x2
+ 2x + 1? (3 marks)
−6x + 2 = 0 1 mark
x = 1/3 1 mark
y = −3 × (1/3)2
+ 2 × (1/3) + 1 = 4/3 1 mark
(c) What is the nature of this stationary point? (2 marks)
d2
y
dx2 = −6 1 mark
−6 < 0 Stationary point is a maximum 1 mark
OR a well reasoned argument involving the shape of x2
and the
negative coefficient.
1
2. (d) Sketch the graph y = −3x2
+ 2x + 1 making sure to label your
sketch clearly. (5 marks)
0.33−0.33 1
1
1.33
x
y
1 mark for each of (−1/3, 0), (1, 0), (0, 1), (0.33, 1.33), 1 mark for
shape.
(e) On different axes sketch the graph y = −3x2
+ 2x − 5. Make sure
to label your sketch clearly. (2 marks)
0.33−5
x
y
1 mark for (0, −5), 1 mark for shape
4. A railway driver notes the number of minutes late his train is over a period
of 13 days.
1 3 2 -1 7 -6 1 1 5 5 4 0 7
(a) What is the mode? (1 marks)
The most common value is 1.
2
3. (b) What is the median? (2 marks)
The ordered data is
-6 -1 0 1 1 1 2 3 4 5 5 7 7
1 mark for table.
13 × 1/2 = 6.5
median is 7th term 2 1 mark for answer.
(c) What is the interquartile range? (3 marks)
13 × 1/4 = 3.25 1
2 mark
Q1 is the 4th term =1 1
2 mark
13 × 3/4 = 9.75 1
2 mark
Q3 is the 10th term =5 1
2 mark
IQ = Q3 − Q1 = 5 − 1 = 4 1 mark
5. Solve the following quadratic equations using the method stated. No
points will be awarded if another method is used. Leave answers
in surd form.
(a) 3x2
− 2x − 2 = 0. Solve by completing the square. (5 marks)
Divide by 3:
x2
− 2
3 x − 2
3 = 0
(x − 1
3 )2
− 1
9 − 2
3 = 0 2 marks
(x − 1
3 )2
= 7
9 1 mark
x − 1
3 = ±
√
7
3 1 mark
x = 1
3 ±
√
7
3 1 mark
(b) −2x2
+ 5x − 1 = 0. Solve by using the quadratic formula. (4
marks)
a = −2, b = 5, c = −1 1 mark for identifying a, b, c
x =
−5±
√
52−4×(−2)×(−1)
2×−2 1 mark
x = 5±
√
17
4 2 marks
(c) x2
+ 4x − 5 = 0. Solve by factorising. (2 marks)
(x + 5)(x − 1) = 0 1 mark
x = −5, x = 1 1 mark
6. (a) Show that there is a solution to x3
− 4x2
− 2x + 1 = 0 for some x
between 0 and 1. (3 marks)
f(x) = x3
− 4x2
− 2x + 1
f(0) = 03
− 4 × 02
− 2 × 0 + 1 = 1 > 0 1 mark
f(1) = 13
− 4 × 12
− 2 × 1 + 1 = −4 < 0 1 mark
f(0) > 0, f(1) < 0 so there is a solution between 0 and 1. 1 mark
3
4. (b) Use the iteration formula xn+1 = −1
x2
n−4xn−2 to find a solution to
2 d.p. (7 marks)
x0 = 0.5
x1 = 0.27
x2 = 0.33
x3 = 0.31
x4 = 0.32
x5 = 0.32
Solution is 0.32 to 2d.p.
1 mark for choice of x0, 4 marks for working, 1 mark for stopping
at a reasonable stage, 1 mark for solution.
7. A food journalist wants to find out if there is a relationship between where
people live and what their favourite food is. She asks 80 people from
around Britain and gets the following data.
England Wales Scotland Ireland
Pizza 1 4 8 6
Curry 8 10 22 4
Fish and Chips 11 4 1 1
(a) State the null hypothesis and the alternative hypothesis. (2
marks)
H0 : There is no correlation. 1 mark
H1 : There is a correlation. 1 mark
(b) What is the χ2
test statistic? (10 marks)
The totals are
England Wales Scotland Ireland Row total
Pizza 1 4 8 6 19
Curry 8 10 22 4 44
Fish and Chips 11 4 1 1 17
Column total 20 18 31 11 80
The fit table is
4.75 4.275 7.3625 2.6125
11 9.9 17.05 6.05
4.25 3.825 6.5875 2.3375
The residual table is
-3.75 -0.275 0.6375 3.3875
-3 0.1 4.95 -2.05
6.75 0.175 -5.5875 -1.3375
The χ2
table is
4
5. 2.9605 0.0177 0.0552 4.3924
0.8182 0.0010 1.4371 0.6946
10.7206 0.0080 4.7393 0.7653
The test statistic is 26.6.
2 marks per table (-0.5 per error), 2 marks for solution.
(c) If we test at a 1% level of significance what is the critical χ2
value?
(2 marks)
Degree of freedom is (4 − 1) × (3 − 1) = 6 1 mark
Critical value is 16.8 1 mark
(d) What can we deduce? (2 mark)
26.8 > 16.8 so there is a correlation between the food people
prefer and the country they live in.
8. A Baker claims there is a mean of 17 cherries in each of his cherry cakes.
A customer buys 9 random cherry cakes and notes how many cherries are
in each one. He writes his test data in a table.
10 15 19 16 1 20 13 15 17
(a) State the null hypothesis and the alternative hypothesis. (2
marks)
H0 : µ = 17 1 mark
H1; µ = 17 1 mark
(b) What is the mean of the test data? (2 marks)
µ(X) = 10 + 15 + 19 + 16 + 1 + 20 + 13 + 15 + 17/9 = 126/9 = 14
1 mark for method, 1 mark for solution.
(c) What is the sample standard deviation of the test data? (4
marks)
(X[i])2
= 100 225 361 256 1 400 169 225 289
σ2
(X) = 100+225+361+256+1+400+169+225+289−9×142
9−1 = 2026−1764
8 =
32.75
σ(X) = 5.723 to 3 d.p. 1 mark for square values, 1 mark for
working, 2 marks for solution.
(d) What is the T test statistic? (3 marks)
µ = 17, µ(X) = 14, σ(X) = 5.723, n = 9.
T = 14−17
5.723/
√
9
= −1.57 to 2 d.p. 1 mark for identifying variables, 1
mark for working, 1 mark for answer.
5
6. (e) The study is taken with a 1% level of significance. What is the
critical T value? (2 marks)
D.f. = 9 − 1 = 8 1 mark
1%, two tailed
Critical values are -3.355 and 3.355. 1 mark
(f) What can we deduce? (2 marks)
−3.355 < −1.57 so we accept the null hypothesis.
9. Consider the following shape.
4
a
60
80
40 b
(a) What is the length a to 2 d.p.? (2 mark)
tan(60) = a
4
a = 4 tan(60) = 4
√
3 = 6.93.
1 mark for working, 1 mark for solution.
(b) What is the area of the above shape to 1 d.p.? (6 marks)
The area of the left triangle is 0.5 × 4
√
3 × 4 = 8
√
3. 2 marks
The third angle in the right triangle is 180 − 80 − 40 = 60. 1
mark
b
sin(60) = 4
√
3
sin(80)
b = 6.09. 1 mark
The area of the right triangle is 0.5×6.09×4
√
3×sin(40) = 13.57
to 2d.p. 1 mark
Total area is 13.57 + 8
√
3 = 27.4 to 1 d.p. 1 mark
6
7. 10. A lady has one 2 pound coin, three 1 pound coins and six 10p coins coins
in her purse. She is considering buying a muffin costing 1.10 and a coffee
costing 80p.
(a) What is the probability that after pulling out 1 coin the lady will
have enough money for the coffee? (1 mark)
P(1) + P(2) = 1/10 + 3/10 = 2/5 1 mark for solution.
(b) What is the probability that after pulling out 2 coins the lady will
have the exact money for the muffin? (2 marks)
Combinations are 1 then a 10p or 10p then 1. P(1, 10p) +
P(10p, 1) = 3/10 × 6/9 + 6/10 × 3/9 = 2/5
1 mark for working, 1 mark for solution.
(c) What is the probability that after pulling out 2 coins the lady will
have enough money for the coffee and the muffin? (4 marks)
Combination of coins 2,1; 2,10p; 1,1. Probability is
2×1/10×3/9+2×1/10×6/9+3/10×2/9 = 4/15 1 mark per probability
and 1 mark for solution.
7
8. Formulae
Let X be a list of data of size n.
Mean:
µ(X) =
n
i=1 X[i]
n
Variance
σ2
(X) =
n
i=1(X[i])2
n
− µ2
(X)
Z-statistic
Z =
µ(X) − µ
σ/
√
n
Sample Variance
σ2
(X) =
n
i=1(X[i])2
− nµ2
(X)
n − 1
T-statistic
T =
µ(X) − µ
σ(X)/
√
n
Alternative notation
Mean
¯x =
x
n
Variance
V ar =
x2
n
− ¯x2
Z-statistic
Z =
¯x − A
σ/
√
n
Sample Variance
s2
=
x2
− n¯x2
n − 1
T-statistic
T =
¯x − A
s/
√
n
8
9. Pythagoras’ Theorem
a2
+ b2
= c2
tan(A) =
opp
adj
, cos(A) =
adj
hyp
, sin(A) =
opp
hyp
Sine rule
a
sin(A)
=
b
sin(B)
=
c
sin(C)
Cosine rule
a2
= b2
+ c2
− 2bc cos(A)
Area
Area = 1/2ab sin(C)
Quadratic formula
x =
−b ±
√
b2 − 4ac
2a
Equation of a straight line
y = mx + c
Gradient of a straight line
m =
y2 − y1
x2 − x1
9
