Daily Practice · Higher Plus
May 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1995 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1995A cuboid measures 14 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd May 1995A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd May 1995A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 4th May 1995Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 5th May 1995Make x the subject of 4x + 6 = y(x + 6).
- 6th May 1995y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 81.
- 7th May 1995The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th May 1995A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 9th May 1995On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th May 1995A rectangle is 17 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th May 1995Write 6/(x + 5) + 5/(x + 2) as a single fraction.
- 12th May 1995A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 13th May 1995In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 14th May 1995The probability of winning a game is 3/4. A player expects 18 wins. How many games did they play?
- 15th May 1995A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 16th May 1995Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 17th May 1995Solve 4x^2 - 4x - 3 = 0.
- 18th May 1995y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 19th May 1995In a vector proof you find that vector PQ = 4a - 4b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 20th May 1995A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 21st May 1995On 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?
- 22nd May 1995A block has mass 270 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd May 1995f(x) = 7x + 3. Work out the inverse function f^-1(x).
- 24th May 1995y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 25th May 1995A cuboid measures 6 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th May 1995A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th May 1995A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 28th May 1995x = 181 and y = 37, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th May 1995Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 30th May 1995y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 64.
- 31st May 1995A cuboid measures 9 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.