Daily Practice · Higher Plus
May 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1996The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 2nd May 1996A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 3rd May 1996On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th May 1996A car covers 220 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.
- 5th May 1996The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 6th May 1996A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 7th May 1996In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 8th May 1996The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?
- 9th May 1996A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 10th May 1996Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 11th May 1996A quadratic sequence starts 2, 16, 38, 68. Work out the second difference, and the coefficient of n^2.
- 12th May 1996y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 13th May 1996In a vector proof you find that vector PQ = a - 2b and vector RS = 3a - 6b. What does this show about PQ and RS?
- 14th May 1996A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 15th May 1996On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th May 1996Simplify sqrt(75) + sqrt(147), giving your answer in the form a sqrt(b).
- 17th May 1996Solve x^2 + x - 6 > 0.
- 18th May 1996y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 19th May 1996A cuboid measures 12 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th May 1996A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st May 1996A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 22nd May 1996A rectangle is 13 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd May 1996Write x^2 - 2x + 2 in the form (x + a)^2 + b.
- 24th May 1996y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 64.
- 25th May 1996A cuboid measures 13 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th May 1996A bag holds 5 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th May 1996On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th May 1996Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 29th May 1996Work out the coordinates of the turning point of y = x^2 - 10x - 4.
- 30th May 1996A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 31st May 1996The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.