MOE Exam Practice

School Exam Revision

Questions modelled on Sec 1 school CA/SA papers — Section A short answers and Section B problem sums with full working shown before the final answer.

Prof. Tan

The Number Realm

The Mid-Year Exam looms! I've compiled questions matching Sec 1 school paper formats: Section A short answers + Section B problem sums.

Learning methods:CRAI-We-YouSpaced reviewRetrievalMetacognition

Section A

2 marks

Express / IP Sec 1 CA1

Q1. Prime Factorisation

Express 180 as a product of its prime factors in index notation.

Divide out 2² and 3

180 \div 4 \div 3 = ?

180 \div 4 = 45

, then

45 \div 3 = 15.

Finish the factorisation

Section A

2 marks

Normal Academic Sec 1

Q2. Integers

Evaluate

(- 4) + (- 7) - (- 10)

Step 1 — Add the first two terms

(- 4) + (- 7) = ?

Step 2 — Subtract (−10)

Section A

2 marks

Normal Academic Sec 1 CA1

Q3. Algebraic Expressions

Simplify

\frac{x}{2} + \frac{x}{4}

fully.

Step 1 — Match denominators

You are adding $\frac{x}{2}$ and $\frac{x}{4}$ . Before adding, both fractions need the same denominator.

$\frac{x}{4}$ already has denominator 4. Rewrite $\frac{x}{2}$ so it also has denominator 4 (multiply the top and bottom of $\frac{x}{2}$ by 2).

Type the complete fraction, e.g. $\frac{2 x}{4}$

Do not type just 2 — that is only the numerator.

Multiply top and bottom of $\frac{x}{2}$ by 2 → Type: $\frac{2 x}{4}$

Step 2 — Add and simplify

Section A

3 marks

Express Sec 1 CA2

Q4. Algebraic Expressions

Simplify

\frac{3 x}{2} - \frac{x}{6}

fully.

Step 1 — Match denominators

You are subtracting $\frac{x}{6}$ from $\frac{3 x}{2}$ . Both fractions need the same denominator.

The lowest common denominator of 2 and 6 is 6. Rewrite $\frac{3 x}{2}$ with denominator 6 (multiply the top and bottom by 3).

Type the complete fraction, e.g. $\frac{9 x}{6}$

Do not type just 9 or $9 x$ .

Multiply top and bottom of $\frac{3 x}{2}$ by 3 → Type: $\frac{9 x}{6}$

Step 2 — Subtract and simplify

Section A

3 marks

Express Sec 1 SA1

Q5. Algebraic Expressions

Simplify 5

(2 x - 3) - 3 (x + 4) + 7

Expand

(2 x - 3) = ?

Expand

Section A

3 marks

School Prelim Sec 1

Q6. Linear Equations

Solve the equation 4

(x - 2) = 3 x + 5.

Expand

(x - 2) = ?

Subtract from both sides

Add to both sides

Section A

2 marks

Normal Academic Sec 1 CA1

Q7. Linear Equations

Solve the equation

\frac{x}{6} = 7.

Multiply both sides

Do the same operation on both sides

\frac{x}{6}

× 6

both sides

× 6

Multiply both sides by 6. What is x?

Section A

3 marks

Express Sec 1 SA1

Q8. Linear Equations

Solve the equation

\frac{x - 3}{4} = 2.

Multiply both sides

Do the same operation on both sides

\frac{x - 3}{4}

× 4

both sides

× 4

Multiply both sides by 4. What is $x - 3$ ?

Add to both sides

Section B

4 marks

School SA2 Sec 1

Q9. Linear Equations

Solve the equation

\frac{2 x}{3} = 14.

Multiply both sides

Do the same operation on both sides

\frac{2 x}{3}

× 3

both sides

× 3

Multiply both sides by 3. What is $2 x$ ?

Divide both sides

Section A

3 marks

Express Sec 1 CA2

Q10. Linear Equations

Solve the equation

\frac{x}{2} + \frac{x}{3} = 5.

Step 1 — Combine the left side

Combine $\frac{x}{2} + \frac{x}{3}$ into one fraction.

Use denominator 6 (the LCM of 2 and 3):

Rewrite $\frac{x}{2}$ as $\frac{3 x}{6}$
Rewrite $\frac{x}{3}$ as $\frac{2 x}{6}$
Add: $\frac{3 x}{6} + \frac{2 x}{6}$

Type one fraction over 6, e.g. $\frac{5 x}{6}$

Do not type just 5.

Add the numerators: $3 x + 2 x = 5 x$ . Type: $\frac{5 x}{6}$

Step 2 — Multiply both sides

Step 3 — Divide both sides

Section B

4 marks

School SA2 Sec 1

Q11. Linear Equations

Solve the equation

\frac{x + 5}{2} + \frac{x}{4} = 7.

Step 1 — Remove fractions

Do the same operation on both sides

\frac{x + 5}{2} + \frac{x}{4}

× 4

both sides

× 4

Multiply every term by 4. What is the right side?

4 \times 7 = 28.

Step 2 — Subtract from both sides

Step 3 — Divide both sides

Section B

5 marks

IP Sec 1

Q12. Linear Equations

Solve the equation

\frac{3 x + 2}{5} = 4.

Multiply both sides

Do the same operation on both sides

\frac{3 x + 2}{5}

× 5

both sides

× 5

Multiply both sides by 5. What is $3 x + 2$ on the left equal to on the right?

Subtract from both sides

Divide both sides

Section A

3 marks

Normal Academic Sec 1

Q13. Inequalities

Solve

\frac{x}{3} - 1 > 2.

Add 1

\frac{x}{3}

> ?

Multiply by 3

Section A

3 marks

Express Sec 1 CA2

Q14. Inequalities

Solve

\frac{x}{2} + 1 \leq 6

and state the largest integer value of

x

Subtract 1

Subtract 1 from both sides:

\frac{x}{2}

≤ ?

Multiply by 2

Section A

2 marks

Normal Academic Sec 1

Q15. Ratio

A sum of $120 is divided between A and B in the ratio 3 : 5. Find B's share.

Parts

Total parts =

3 + 5 = ?

One part

Section A

2 marks

Express Sec 1

Q16. Angles

In the diagram, AB ∥ CD. Angle AEF = 65°. Find angle EFD (alternate angles).

Final answer

Section A

3 marks

Sec 1 CA2

Q17. Statistics

The marks of 5 students are 6, 8, 7, 9, 5. Find the mean mark.

Sum

Sum =

6 + 8 + 7 + 9 + 5 = ?

Section B

5 marks

School SA2 Sec 1

Q18. Word Problems

A shop sells apples at $0.80 each and oranges at $1.25 each. Tom bought 5 apples and some oranges for $14. How many oranges did he buy?

Apples cost

Cost of 5 apples = 5 × $

0.80 = ?

Oranges cost

Number

Section B

4 marks

Express Sec 1 SA2

Q19. Pythagoras' Theorem

A right-angled triangle has legs 9 cm and 12 cm. Find the length of the hypotenuse.

Theorem

c^{2} = 9^{2}

1 2^{2}

81 + 144 = ?

Section B

4 marks

IP Sec 1

Q20. Inequalities

Solve 2

(x + 1) \leq 3 x - 4

and state the smallest integer value of

x

Expand

2 x + 2 \leq 3 x - 4.

Rearrange: 6 ≤ ?

Section A

2 marks

Express Sec 1 CA1

Q21. Expanding Brackets

Expand 3(

2 x + 5

Final answer

Section A

2 marks

Normal Academic Sec 1 CA1

Q22. Expanding Brackets

Expand −(

x + 4

Flip signs

- (x) = ?

and

- (+ 4) = ?

Section A

3 marks

Express Sec 1 CA2

Q23. Expanding Brackets

Expand −3(

x - 2

Multiply x

- 3 \times x = ?

Multiply −2

Section B

4 marks

School SA2 Sec 1

Q24. Expanding Brackets

Expand and simplify 4

(x - 1) - 2

(

x + 3

Expand first

(x - 1) = ?

Expand second

Combine

Section B

5 marks

IP Sec 1

Q25. Expanding Brackets

Expand and simplify −

(5 x - 2) + 3 (x + 1) - 2

(

x - 4

Expand each part

- (5 x - 2) = ?

Second bracket

Third bracket

Section A

2 marks

Normal Academic Sec 1

Q26. Factorisation

Factorise completely:

12 a - 18.

HCF

The highest common factor of 12 and 18 is ?

Section A

2 marks

Normal Academic Sec 1 CA1

Q27. Number Patterns

Write down the next two terms of the sequence 6, 11, 16, 21, …

Difference

Common difference =

11 - 6 = ?

Next term

Section A

3 marks

Express Sec 1 CA2

Q28. Number Patterns

The nth term of a sequence is

3 n + 2.

Find the 9th term.

Substitute

(9) + 2 = ?

Section A

3 marks

Sec 1 CA2

Q29. Number Patterns

In the sequence 7, 13, 19, 25, …, find the term number of the value 55.

Difference

Common difference = ?

Solve

Section B

4 marks

School SA2 Sec 1

Q30. Number Patterns

A pattern of dots forms rows: Row 1 has 4 dots, Row 2 has 7, Row 3 has 10. (a) How many dots in Row 8? (b) Write the nth term.

(a) Row 8

Difference 3. Row

8 = 4 + 7 (3) = ?

(b) nth term

Section B

5 marks

IP Sec 1

Q31. Number Patterns

Sequence

A

: 5, 9, 13, 17, … Sequence

B

: 2, 4, 8, 16, … Find the 6th term of A minus the 5th term of

B

6th term of A

5 + 5 (4) = ?

5th term of B

Difference

Section A

2 marks

Normal Academic Sec 1 CA1

Q32. Percentages

Express 3/5 as a percentage.

Decimal

3 \div 5 = ?

Section A

2 marks

Express Sec 1

Q33. Percentages

Find 15% of 240.

Calculate

0.15 \times 240 = ?

Section A

3 marks

Sec 1 CA2

Q34. Percentages

A shirt costs $80. During a sale, the price is reduced by 25%. Find the sale price.

Discount

25% of

80 = ?

Sale price

Section B

4 marks

School SA2 Sec 1

Q35. Percentages

After a 20% discount, a pair of shoes costs $96. Find the original price.

Sale is 80%

96 = 80

% of original.

96 \div 0.8 = ?

Section B

5 marks

IP Sec 1

Q36. Percentages

A quantity increases by 10% and then decreases by 10% on the new value. If the final value is $990, find the original value.

Net multiplier

×1.10 then ×0.90 = ×0.99. So final = 0.99 × original.

Original

Section A

3 marks

Normal Academic Sec 1 SA2

Q37. Percentages

In a test, 42 out of 56 students passed. Find the pass rate as a percentage.

Fraction

42 \div 56 = ?

(decimal)