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higher mathematic papers for revision
Typology: Cheat Sheet
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Topics: Simultaneous Equations, Sequences, Quadratics, Trigonometry, Sine Rule, Cosine Rule, Straight Line Graphs
Answer all questions. Show full working. Give answers to an appropriate degree of accuracy.
Q1 Straight Line Graphs (6 marks)
State the gradient and y-intercept of y = -4x + 7.
Find y when x = -3.
Find x when y = 19.
Q2 Straight Line Graphs (7 marks)
Find the intersection of y = 3x - 2 and y = -2x + 13.
Verify your solution.
Q3 Sequences (6 marks)
Sequence: 7, 12, 17, 22, ...
Write the next two terms.
Find the nth term.
Find the 50th term.
Q4 Sequences (7 marks)
The nth term is 5n − 8.
Write the first five terms.
Determine whether 147 is in the sequence.
Q10 Trigonometry (6 marks)
A tree casts a shadow 11 m long. The angle of elevation of the sun is 54°.
Find the height of the tree.
Q11 Sine Rule (7 marks)
In triangle ABC, A=52°, B=71°, a=12 cm.
Find side b.
Q12 Cosine Rule (8 marks)
Two sides are 16 cm and 21 cm with included angle 63°.
Find the third side.
Q1: Gradient = -4, y-intercept = 7, y = 19, x = -
Q2: (3,7)
Q3: 27, 32; nth term = 5n + 2; 252
Q4: -3, 2, 7, 12, 17; 147 is a term (n=31)
Q5: x = 5, y = 3
Q6: x = 5, y = 3
Q7: x = 4 or x = 5
Q8: x ≈ 2.79 or -0.
Q9: 10.8 cm
Q10: 15.1 m
Q11: b ≈ 15.3 cm
Q12: third side ≈ 18.9 cm
