Why settle the sign before calculating?

For directed numbers, decide the sign first and then work with the magnitudes: same signs add and keep the sign, opposite signs take the sign of the larger magnitude, and multiplication or division gives positive for like signs and negative for unlike signs.

What order should be used when substituting?

Put brackets round every substituted value, then work through brackets, indices, multiplication and division, and finally addition and subtraction. Keep −3² (which is −9) apart from (−3)² (which is 9).

S1 Maths: Directed Numbers and Algebra (Intermediate, 10 Questions)

2026-11-06

Tutor Prep Guide · S1 Mathematics

Ten intermediate items on mixed operations and brackets: sign rules in chained multiplication and division, telling -3 squared from (-3) squared, negative indices, flipping signs when a minus sign precedes a bracket, substitution with two letters and a simple linear equation.

Quick answer Answers in order: -8, 18, 1, 2x + 7, 2a + 6, 18, -4, -3 °C, 11 – 3x, x = 5. Flipping every sign inside the bracket is where most marks are lost.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 35 minutes
Difficulty mix	Intermediate 10
Chapter	Chapter: S1 Maths: Directed Numbers and Algebra
Level	S1

02 Questions (10 items)

IntermediateWork out (-4) x (-6) / (-3).
IntermediateBy how much do minus 3 squared and (-3) squared differ?
IntermediateWork out (-2) cubed plus (-3) squared.
IntermediateSimplify 4x – (2x – 7).
IntermediateSimplify 2(3a – 1) – 4(a – 2).
IntermediateFind the value of a squared times b minus ab when a = -2 and b = 3.
IntermediateFind the sum of -7, 5 and -2.
IntermediateThe temperature rises by 15 °C from -6 °C and then falls by 12 °C. Find the final temperature.
IntermediateSimplify 5 – 3(x – 2).
IntermediateSolve the equation 3x + 4 = 19.

03 Answers and one-line notes

#	Answer	One-line note
1	-8	The product of two negatives is 24, and dividing 24 by -3 gives -8.
2	18	Minus 3 squared squares only the 3 and gives -9, while (-3) squared gives 9, so they differ by 18.
3	1	(-2) cubed is -8 and (-3) squared is 9, so the sum is 1.
4	2x + 7	A minus sign before the bracket flips every sign inside: 4x – 2x + 7 gives 2x + 7.
5	2a + 6	Expanding gives 6a – 2 – 4a + 8, and collecting like terms gives 2a + 6.
6	18	a squared is 4, so 4 x 3 = 12, while ab = -6, and 12 – (-6) = 18.
7	-4	First -7 + 5 = -2, then -2 + (-2) = -4.
8	-3 °C	From -6 °C the temperature reaches 9 °C, and 9 – 12 gives -3 °C.
9	11 – 3x	Expanding gives 5 – 3x + 6, so the answer is 11 – 3x; the minus sign reaches every term in the bracket.
10	x = 5	Subtract 4 from both sides to get 3x = 15, then divide by 3 to get x = 5.

04 What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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