Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
15 questions · official format, shuffled order
1 What is the gradient of the line through (−4, 5) and (2, −7)?
Show worked solution
−12 ÷ 6 = −2. (−0.5 is run over rise.)
2 What is the midpoint of (−3, 8) and (9, −2)?
Show worked solution
((−3 + 9) ÷ 2, (8 + (−2)) ÷ 2) = (3, 3). ((6, 6) adds without halving.)
3 How long is the interval from (−1, −2) to (11, 3)?
Show worked solution
√(122 + 52) = √169 = 13. (17 adds the across and up instead of using Pythagoras.)
4 Which line has gradient 4 and passes through (2, −1)?
Show worked solution
−1 = 8 + c, so c = −9: y = 4x − 9. (y = 4x + 7 uses −1 − 8 as +7 — a sign slip.)
5 Write 6x + 2y = 10 in gradient–intercept form. What are the gradient m and the y-intercept c?
Show worked solution
y = −3x + 5, so m = −3, c = 5. (m = −3, c = 10 forgets to divide the 10 by 2.)
6 What is the gradient of a line perpendicular to 5x − 2y = 8?
Show worked solution
y = (5/2)x − 4 has gradient 5/2, so a perpendicular gradient is −2/5. (−5/2 changes the sign but does not flip the fraction.)
7 A line passes through (−2, 3) and (4, 15). Where does it cross the x-axis?
Show worked solution
m = 2 and y = 2x + 7. Setting y = 0 gives x = −3.5. (x = −7 forgets to divide by 2.)
8 The line 5x + 2y = 20 and the two axes form a triangle. What is its area?
Show worked solution
Intercepts (4, 0) and (0, 10), so area = ½ × 4 × 10 = 20.
9 Which line passes through (2, −4) and is parallel to y = −3x − 4?
Show worked solution
−4 = −6 + c, so c = 2: y = −3x + 2. (y = −3x − 10 adds the 6 the wrong way: −4 − 6.)
10 The line through (1, k) and (5, 9) has gradient 3. What is k?
Show worked solution
9 − k = 12, so k = −3.
11 Three statements about the line 4x + 5y = 20:
1 It passes through (0, 4).
2 Its gradient is 4/5.
3 It crosses the x-axis at (5, 0).
Which statements are correct?
1 It passes through (0, 4).
2 Its gradient is 4/5.
3 It crosses the x-axis at (5, 0).
Which statements are correct?
Show worked solution
x = 0 gives y = 4 (1 ✓). y = −(4/5)x + 4, so the gradient is −4/5, not 4/5 (2 ✗). y = 0 gives x = 5 (3 ✓). 1 and 3.
12 A is (3, k) and B is (9, −2). The length of AB is 10. Which of these could k be?
Show worked solution
k − (−2) = 8 or −8, so k = 6 or k = −10. Of the options only 6 works. (−6 uses k − 2 = −8, dropping the minus on B’s y-value.)
13 Which equation describes the line shown?
Show worked solution
It meets the y-axis at 4 and falls 4 over a run of 6: gradient −2/3. y = −(2/3)x + 4. (y = −(2/3)x + 6 uses the x-intercept as c.)
14 A(0, 0), B(4, 2), C(3, 4) and D(−1, 2) are joined in order. What is ABCD?
Show worked solution
AB and CD have gradient ½; BC and DA have gradient −2. Opposite sides are parallel and ½ × −2 = −1, so every corner is a right angle. AB = √20 but BC = √5, so it is a rectangle that is not a square.
15 P is (−5, −1) and Q is (3, 5).
1 The midpoint of PQ is (−1, 2).
2 The gradient of PQ is 3/4.
3 The perpendicular bisector of PQ has gradient 4/3.
Which statements are correct?
1 The midpoint of PQ is (−1, 2).
2 The gradient of PQ is 3/4.
3 The perpendicular bisector of PQ has gradient 4/3.
Which statements are correct?
Show worked solution
((−5 + 3) ÷ 2, (−1 + 5) ÷ 2) = (−1, 2) (1 ✓). 6 ÷ 8 = 3/4 (2 ✓). The perpendicular gradient is −4/3, not 4/3 (3 ✗). 1 and 2.