Daily Practice · Higher Plus
May 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2004In a vector proof you find that vector PQ = a + 5b and vector RS = 4a + 20b. What does this show about PQ and RS?
- 2nd May 2004A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 3rd May 2004A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 4th May 2004Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 5th May 2004Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 6th May 2004y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 9.
- 7th May 2004A cuboid measures 4 cm by 8 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th May 2004A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th May 2004On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th May 2004A block has mass 890 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.
- 11th May 2004Use the iteration x(n+1) = cube root of (2x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 12th May 2004A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 13th May 2004A cuboid measures 4 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th May 2004A bag holds 5 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th May 2004A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 16th May 2004x = 96 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th May 2004Work out the nth term of the quadratic sequence 9, 23, 45, 75, ...
- 18th May 2004y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 19th May 2004The 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.
- 20th May 2004A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 21st May 2004On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 22nd May 2004A car covers 500 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd May 2004The point (-6, 1) lies on y = f(x). Write down its image on y = f(x) - 2.
- 24th May 2004y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 25th May 2004In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 26th May 2004The probability of winning a game is 1/4. A player expects 16 wins. How many games did they play?
- 27th May 2004A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 28th May 2004Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 29th May 2004Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 30th May 2004y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 16.
- 31st May 2004In a vector proof you find that vector PQ = 2a + 3b and vector RS = 10a + 15b. What does this show about PQ and RS?