Paradigm Specialising in O & A Level Mathematics

Name: School: Target Grade:

SECONDARY 1 WA2
MOCK EXAM PAPER

READ THESE INSTRUCTIONS FIRST

INSTRUCTIONS TO CANDIDATES

1. Find a nice comfortable spot without distraction.

2. Be fully focused for the whole duration of the test.

3. Speed is KING. Finish the paper as soon as possible then return-back to Check Your Answers.

4. As you are checking your answers, always find ways to VALIDATE your answer.

5. Avoid looking through line by line as usually you will not be able to see your Blind Spot.

6. If there is no alternative method, cover your answer and REDO the question.

7. Give non-exact answers to 3 significant figures, or 1 decimal place for angles in degree, or 2
decimal place for $$$, unless a different level of accuracy is specified in the question.

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 Paradigm Specialising in O & A Level Mathematics

Name: ____________________________ Class: ______ Date: _________

Secondary 1 Mathematics
WA2 Mock Paper
Topic:
Duration: 1 hour

Estimation & Approximation

40
1 (a) Round off 3025.378 to
(i) 2 decimal places, [1]
(ii) 2 significant figures. [1]
(b) Round off 0.03288345 to 3 significant figures. [1]
(c) Without the use of calculator, estimate the value of
3
√999
(i) × 5.01,
9.8
[1]
√65
(ii) 3 × 19.9. [1]
√9

2 Use a calculator to evaluate 3(√2020−3.143 ) correct to

3
500( √65)

(a) 4 significant figures.

(b) 3 decimal places. [1]
[1]

3 (a) By rounding the numbers to 1 significant figure, estimate the value [2]
√101.3×64.231
of . Show your working clearly.
(1.98)3

(b) Without using the calculator, determine whether the value found in (a) is an [1]
over or under estimation. Give a reason for your answer.

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 Paradigm Specialising in O & A Level Mathematics

Algebra

1 Simplify the following.

(a) 5(𝑥 + 3𝑦) + 3(4𝑥 − 2𝑦), [2]
2𝑝−3𝑞 3𝑝−5𝑞 [2]
(b) − .
5 4

2 Solve the following equations.

2𝑥
(a) 3 = −54, [2]
(b) 6(𝑥 − 1) − 2(𝑥 + 2) = 12. [2]

3 (a) 𝑤 = 1 (𝑎2 + 𝑏). Find the value of w if 𝑎 = −2 𝑎𝑛𝑑 𝑏 = 3. [2]

3
32
(b) Solve 𝑥−3 = 8.
[2]

4 Simplify the following expressions.

4 − 3[2 − (3 − 2𝑦)]
[2]

5 Factorise the following expressions completely.

(a) 25𝑚𝑝 − 40𝑚𝑚
[1]
(b) −18𝑎𝑥 + 24𝑎𝑦 − 6𝑎 [1]
(c) 5𝑢(2𝑣 − 3) − 2(6𝑣 − 9) [2]

6 Write an algebraic expression, in its simplest form, for each of the following
statements.
(a) Divide 2𝑡 𝑏𝑦 4𝑣. [1]
(b) Add 15 to the product of h and m. [1]
(c) Subtract 3𝑐 + 2 from the sum of 2c and 3. [1]

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 Paradigm Specialising in O & A Level Mathematics

Algebra (Word Problem)

1 A ticket for an adult visiting the Universal Studios costs p dollars.

A ticket for a child costs $8 less than an adult’s ticket.
(a) Write an expression in terms of p for the cost of a child’s ticket. [1]
(b) (i) Jason bought 2 adult tickets and 4 child tickets. Write down and [2]
simplify an expression, in terms of p, for the cost of the 6 tickets.
(ii) If the price of an adult ticket is $50, find the total cost Jason has to pay for [2]
the 6 tickets.

2 Mary is x years old and James is 8 years older than her.

Their mother is 3 times as old as Mary and their father is twice as old as James.
(a) Write down expressions, in terms of x, for
(i) Jame’s age, [1]
(ii) their father’s age [1]
(b) Given that the sum of the ages of the four members of the family is 129, [2]
find Mary’s age.

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 Paradigm Specialising in O & A Level Mathematics

Answer Key

Estimation & Approximation

1 (a) Round off 3025.378 to

(i) 2 decimal places,
(ii) 2 significant figures.
(b) Round off 0.03288345 to 3 significant figures.
(c) Without the use of calculator, estimate the value of
3
√999
(i) × 5.01,
9.8
√65
(ii) 3 × 19.9.
√9
Solutions:
3
√999 √65
(c)(i) × 5.01 (ii) 3 × 19.9
9.8 √9
3 √64
√1000 ≈ × 20
≈ × 5 3
√8
10
8
10 = 2 × 20
= 10 × 5
= 80
=5
Ans: (ai) 3025.38(2d.p) (aii) 3000 (2s.f) (b) 0.0329 (2s.f) (ci) 5 (cii) 80
2
3(√2020−3.143 )
Use a calculator to evaluate 3 correct to
500( √65)

(c) 4 significant figures.

(d) 3 decimal places.
Ans: (a) 0.02087, (b) 0.021
3 (a) By rounding the numbers to 1 significant figure, estimate the value
√101.3×64.231
of . Show your working clearly.
(1.98)3

(b) Without using the calculator, determine whether the value found in (a) is an
over or under estimation. Give a reason for your answer.
Solution:
√101.3×64.231 10×60
(a) =
(1.98)3 8

= 75
Ans: (a) 75, (b) Underestimate. The numbers in the numerator have been rounded
down and the number in the denominator has been rounded up,
making the final answer smaller than the actual value.

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 Paradigm Specialising in O & A Level Mathematics

Algebra

1 Simplify the following.

(a) 5(𝑥 + 3𝑦) + 3(4𝑥 − 2𝑦),
2𝑝−3𝑞 3𝑝−5𝑞
(b) − .
5 4

Solutions:
4(2𝑝−3𝑞)−5(3𝑝−5𝑞)
(a) 5𝑥 + 15𝑦 + 12𝑥 − 6𝑦 (b) 20
8𝑝−12𝑞−15𝑝+25𝑞
= 17𝑥 + 9𝑦 (b) = 20
−7𝑝+13𝑞
=
−7𝑝+13𝑞 20
Ans: (a) 17𝑥 + 9𝑦 (b) 20

2 Solve the following equations.

2𝑥
(a) 3 = −54,
(b) 6(𝑥 − 1) − 2(𝑥 + 2) = 12.

Solutions:
2𝑥
(a) 3 = −54, (b) 6(𝑥 − 1) − 2(𝑥 + 2) = 12,
6𝑥 − 6 − 2𝑥 − 4 = 12
2𝑥 = −162 4𝑥 − 10 = 12
𝑥 = −81 4𝑥 = 22
1
𝑥 = 5 ∕ 5.5
2
1
Ans: (a) 𝑥 = −81 (b) 𝑥 = 5.5/5 2

3 Solutions:
1
(a) 𝑤 = 3 [(−2)2 + 3)] (b) 32 = 8(𝑥 − 3)
32 = 8𝑥 − 24
7
=3 8𝑥 = 56
𝑥=7
7
Ans: (a) 𝑤 = 3, (b) 𝑥 = 7

4 Solution:
4 − 3[2 − 3 + 2𝑦]
= 4 − 3(2𝑦 − 1)
= 4 − 6𝑦 + 3
= 7 − 6𝑦
Ans: 7 − 6𝑦
5 Solutions:

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 Paradigm Specialising in O & A Level Mathematics

(c) 5𝑢(2𝑣 − 3) − 6(2𝑣 − 3)

= (5𝑢 − 6)(2𝑣 − 3)

Ans: (a) 5𝑚(5𝑝 − 8𝑛) (b) 6𝑎(−3𝑥 + 4𝑦 − 1) (c) (5𝑢 − 6)(2𝑣 − 3)

6 Ans: (a) 𝑡 , (b) ℎ𝑚 + 15, (c) −𝑐 + 1
2𝑣

Algebra (Word Problem)

1 Solutions:
(b)(i) 2𝑝 + 4(𝑝 − 8) (b)(ii) Total cost
= 2𝑝 + 4𝑝 − 32 = 6(50) − 32
= $(6𝑝 − 32) = $268
Ans: (a) $(𝑝 − 8) (bi) $(6𝑝 − 32) (bii) $268
2 Solutions:
(a)(ii) 2(𝑥 + 8) = 2𝑥 + 16 years old
(b) 𝑥 + 𝑥 + 8 + 3𝑥 + 2𝑥 + 16 = 129
7𝑥 + 24 = 129
𝑥 = 15

Ans: (a) (𝑥 + 8) years old (aii) 2𝑥 + 16 years old (b) Mary’s age is 15 years old.

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