CAPRICORN SOUTH DISTRICT
GRADE 10
MATHEMATICS TEST 2
AUGUST 2024
Duration: 2 Hours Marks: 100
This question paper consists of 7 pages, including the cover page
Mathematics Grade 10 Controlled Test 2 August 2024
CAPS
INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.
1. This task paper consists of 7 Questions.
2. Answer All the questions.
3. Diagrams are not necessarily drawn to scale.
4. Clearly show ALL steps you have used in determining your answers.
5. Approved non – programmable and non - graphical calculators may be used.
6. Answers only will NOT necessarily be awarded full marks.
7. Round off answers to TWO decimal places, unless otherwise stated.
8. Number your answers correctly according to the numbering system used in this question paper.
9. Write legibly and present your work neatly.
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Mathematics Grade 10 Controlled Test 2 August 2024
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QUESTION 1
1.1 Simplify the following expressions fully. Leave your answers with a positive exponent where
necessary:
1.1.1 – 2 (x – 7) (2)
1.1.2 (3x – 5)2 (3)
1.1.3 (x – 3) (x2 + 3x + 9) (2)
p p
1.1.4 + 1 − 1 (2)
5 5
1.2 Factorise fully:
1.2.1 3p – 15 (1)
1.2.2 2x2 – 3x – 5 (2)
1.2.3 a2 – 2ab +b2 – 64c2 (3)
1.3 Given: m = √𝑏 2 − 4𝑎𝑐
1.3.1 Determine the value of m if a = 2, b = – 3 and c = – 1. Leave your answer in simplest
surd form. (2)
1.3.2 State whether m is rational, irrational or non-real. (1)
1.3.3 Between which TWO consecutive integers does m lie? (1)
[19]
QUESTION 2
2.1 Solve for x:
2.1.1 3x – 11 = 0 (2)
2.1.2 2x 2 − x = 6 (4)
1
2.1.3 5𝑥 = 125 (2)
𝑥
2.2 The following inequality is given: 2 + 1 < 3(𝑥 + 7)
2.2.1 Solve for x in the inequality. (3)
2.2.2 Represent your answer to QUESTION 2.2.1 on a number line. (1)
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Mathematics Grade 10 Controlled Test 2 August 2024
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2.3 Solve for 𝑥 and 𝑦 simultaneously:
2𝑥 + 𝑦 = 6 and 4𝑥 + 3𝑦 = 10 (5)
[17]
QUESTION 3
3.1 A right-angled triangle has sides a, b and c and the angle 𝜃, as shown below.
3.1.1 Write the following in terms of a, b and c:
(a) cos (1)
(b) tan (1)
(c) sin (90 − ) (2)
3.1.2 If it is given that a = 5 and = 50 , calculate the numerical value of b. (3)
3.2 In the diagram below, ABC, ACD and ADE are right-angled triangles. 𝐵𝐴̂𝐸 = 900 and 𝐵𝐴̂𝐶 = 300 .
BC = 20 units and AD = 60 units.
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Mathematics Grade 10 Controlled Test 2 August 2024
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Calculate the:
3.2.1 length of AC (2)
3.2.1 size of 𝐶𝐴̂𝐷 (2)
3.2.3 length of DE (3)
[14]
QUESTION 4
4.1 Refer to ∆ ABC below, with sides of length a, b, c and vertical height h.
C
a
b
h
A B
c
4.1.1 Write down sin A in terms of b and h. (1)
4.1.2 Write down sin B in terms of a and h. (1)
sin 𝐴 sin 𝐵
4.1.3 Hence show that = (3)
𝑎 𝑏
4.2 From A on top of a building 50 m high, the angle of elevation of B on a taller building is 340.
If the buildings are 75, 8 m apart, how high is B above street level? (5)
[10]
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Mathematics Grade 10 Controlled Test 2 August 2024
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QUESTION 5
RQ is a vertical pole. The foot of the pole, Q, is on the same horizontal plane as P and S. the pole is anchored
with wire cables RS and RP. The angle of depression from the top of the pole to the point P is 470. PR is 21m
and QS is 17m. RP ̂Q = θ
5.1 Write down the size of θ. (2)
5.2 Calculate the length of RQ. (3)
5.3 Hence, calculate the size of Ŝ (2)
5.4 If P, Q and S lie in a straight line, how far apart are the anchors of the wire cables? (4)
[11]
QUESTION 6
6.1 The marks in a class test of 15 girls in Mr Rudy’s Mathematics class given below. The test is out of
50 marks:
𝟒𝟑 𝟒𝟐 𝟑𝟏 𝟑𝟐 𝟐𝟐 𝟏𝟑 𝟒𝟒 𝟑𝟖 𝟐𝟓 𝟓𝟎 𝟗 𝟏𝟓 𝟐𝟓 𝟑𝟓 𝟒𝟏
6.1.1 Determine the:
(a) mean (3)
(b) median (2)
(c) mode of the marks. (1)
6.1.2 Calculate interquartile range for the class (2)
6.1.3 Draw a box and whisker plot to represent the marks (3)
6.1.4 State whether the test was difficult or not. Give justification for your answer. (3)
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Mathematics Grade 10 Controlled Test 2 August 2024
CAPS
6.2 Consider the box-and-whisker diagrams below representing the marks of two Grade 10 classes in a
test out of 50.
6.2.1 Write down the five number summary for Class 10B. (3)
6.2.2 What is the interquartile range for Class 10A? (2)
6.2.3 What % of marks in 10A lies between the highest mark and the median? (2)
[20]
QUESTION 7
The pulse rate of patients (in beats per minute) at a clinic was measured and the results tabulated in a
frequency table shown below:
7.1 Complete the frequency table (3)
7.2 Use the frequency table to determine:
7.2.1 the total number of patients that were measured on that day (1)
7.2.2 the estimated mean (2)
7.2.3 the modal class (1)
7.2.4 the percentage of patients whose pulse rate was at least 160 beats per minute. (2)
[9]
TOTAL: 100
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