Daily Practice · Higher Plus
May 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2002A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 2nd May 2002A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 3rd May 2002Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 4th May 2002Write 5/(x + 3) + 5/(x + 5) as a single fraction.
- 5th May 2002y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 6th May 2002In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 7th May 2002The probability of winning a game is 4/5. A player expects 32 wins. How many games did they play?
- 8th May 2002On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th May 2002Simplify sqrt(20) + sqrt(125), giving your answer in the form a sqrt(b).
- 10th May 2002Solve 4x^2 + 16x + 15 = 0.
- 11th May 2002y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 12th May 2002In a vector proof you find that vector PQ = 6a - 5b and vector RS = 18a - 15b. What does this show about PQ and RS?
- 13th May 2002A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 14th May 2002A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 15th May 2002A rectangle is 12 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th May 2002f(x) = 8x - 12. Work out the inverse function f^-1(x).
- 17th May 2002y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 49.
- 18th May 2002A cuboid measures 14 cm by 13 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th May 2002A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th May 2002On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st May 2002Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 22nd May 2002Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 23rd May 2002A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 24th May 2002A cuboid measures 9 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th May 2002A bag holds 5 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th May 2002A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 27th May 2002A block has mass 700 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th May 2002Use the iteration x(n+1) = cube root of (9x(n) + 6) with x(0) = 4. Work out x(1) to 3 decimal places.
- 29th May 2002y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 30th May 2002The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 31st May 2002A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.