⚠ Tricky: (x³)² = x⁶ (multiply exponents), then subtract 1 for x⁻¹. Many students add 3+2 instead of multiplying.
Worked Example
(y²)³ × y⁻² = y⁶ × y⁻² = y^(6−2) = y⁴
Memory Point · SLOPE = rise/run = (y₂−y₁)/(x₂−x₁) → always subtract in the same order
Question 09
Slope of a Line
Find the slope of the line passing through (2, −1) and (−4, 5).
⚠ Tricky: If you mix up which point is (x₁,y₁), you still get the same slope — but mixing up x and y order gives a wrong sign.
Worked Example
Points: (1,3) and (4,9)
m = (9−3)/(4−1) = 6/3 = 2
Memory Point · DISTRIBUTIVE: a(b+c) = ab+ac · FOIL for (a+b)(c+d) = ac+ad+bc+bd
Question 10
Distributive Property
Expand: −3(2x − 5) + 4x
⚠ Most missed: forgetting to distribute the negative sign to BOTH terms inside. −3 × (−5) = +15, not −15!
Worked Example
−2(3a − 4) + 5a
= −6a + 8 + 5a
= −a + 8
Chapter 2Geometry
0 / 10 correct
Memory Point · TRIANGLE ANGLES: all 3 angles add up to EXACTLY 180°
Question 01
Triangle Angle Sum
A triangle has angles of 47° and 83°. What is the third angle?
⚠ Tricky: Students sometimes subtract from 360° (that's for quadrilaterals!)
Worked Example
Two angles: 55° and 75°
Third angle = 180° − 55° − 75° = 50°
Memory Point · PYTHAGOREAN THEOREM: a² + b² = c² · c is always the HYPOTENUSE (longest side)
Question 02
Pythagorean Theorem
A right triangle has legs of 9 cm and 12 cm. What is the length of the hypotenuse?
⚠ Tricky: c = √(81+144) = √225. Don't forget to take the square root at the end!
Worked Example
Legs: 3 and 4
c² = 3² + 4² = 9 + 16 = 25
c = √25 = 5
Memory Point · AREA of CIRCLE = π r² · CIRCUMFERENCE = 2πr · r = radius (not diameter!)
Question 03
Circle: Area & Circumference
A circle has a diameter of 10 m. What is its area? (Use π ≈ 3.14)
⚠ Most common mistake: using diameter instead of radius! r = d ÷ 2 = 5.
Worked Example
Diameter = 8 cm → radius = 4 cm
Area = π × 4² = 3.14 × 16 = 50.24 cm²
Memory Point · COMPLEMENTARY = two angles sum to 90° · SUPPLEMENTARY = two angles sum to 180°
Question 04
Complementary & Supplementary Angles
Angle A and Angle B are supplementary. If Angle A = 67°, what is Angle B?
⚠ Tricky: Supplementary → 180°. Students often subtract from 90° (that's complementary!)
Worked Example
Supplementary pair: Angle X = 45°
Angle Y = 180° − 45° = 135°
Memory Point · PERIMETER = sum of ALL sides · AREA = space INSIDE the shape
Question 05
Area of Triangle
A triangle has a base of 14 cm and a height of 9 cm. Find its area.
⚠ Tricky: Area of triangle = ½ × base × height. Students forget the ½ and get double the answer!
Worked Example
Base = 10, Height = 6
Area = ½ × 10 × 6 = 30 cm²
Memory Point · VERTICAL ANGLES: opposite angles when two lines cross → ALWAYS equal
Question 06
Parallel Lines & Transversals
Two parallel lines are cut by a transversal. One angle is 125°. What is the measure of its alternate interior angle?
⚠ Tricky: Alternate interior = equal. Co-interior (same-side) = supplementary (adds to 180°). Don't mix them up!
Worked Example
Alternate interior angles are equal.
If one = 70°, the other = 70°.
Memory Point · VOLUME of RECTANGULAR PRISM = length × width × height (3 dimensions)
Question 07
Volume of a Prism
A rectangular box is 8 cm long, 5 cm wide, and 3 cm tall. What is its volume?
⚠ Tricky: Volume uses ALL THREE dimensions. Students sometimes only multiply two (getting area, not volume).
Worked Example
Box: 4×6×2
V = 4×6×2 = 48 cm³
Memory Point · CONGRUENT: same shape AND same size · SIMILAR: same shape, different size (proportional sides)
Question 08
Similar Triangles
Two similar triangles have corresponding sides in a ratio of 3:5. The smaller triangle has a side of 9 cm. What is the corresponding side of the larger triangle?
⚠ Tricky: Set up the ratio carefully. 3/5 = 9/x, then cross-multiply.
Worked Example
Ratio 2:7, smaller side = 6
2/7 = 6/x → 2x = 42 → x = 21
Memory Point · EXTERIOR ANGLE of TRIANGLE = sum of the two NON-adjacent interior angles
Question 09
Exterior Angle Theorem
In a triangle, two interior angles are 42° and 61°. What is the measure of the exterior angle at the third vertex?
⚠ Tricky: Exterior angle = sum of the two non-adjacent angles. Many students compute 180°−(42°+61°) then subtract again!