Daily Practice · Higher Plus
July 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1996A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 2nd July 1996On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd July 1996A rectangle is 9 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th July 1996f(x) = 5x - 11. Work out the inverse function f^-1(x).
- 5th July 1996y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 6th July 1996In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 7th July 1996The probability of winning a game is 7/8. A player expects 63 wins. How many games did they play?
- 8th July 1996A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 9th July 1996Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 10th July 1996Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 11th July 1996y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
- 12th July 1996In a vector proof you find that vector PQ = 6a + 5b and vector RS = 12a + 10b. What does this show about PQ and RS?
- 13th July 1996A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 14th July 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?
- 15th July 1996A block has mass 420 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th July 1996Use the iteration x(n+1) = cube root of (2x(n) + 9) with x(0) = 4. Work out x(1) to 3 decimal places.
- 17th July 1996A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 18th July 1996A cuboid measures 6 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th July 1996A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th July 1996A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 21st July 1996x = 42 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd July 1996Work out the nth term of the quadratic sequence 3, 5, 9, 15, ...
- 23rd July 1996y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 24th July 1996A cuboid measures 6 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th July 1996A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th July 1996On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th July 1996A car covers 710 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th July 1996The point (4, -6) lies on y = f(x). Write down its image on y = f(x) + 1.
- 29th July 1996y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 30th July 1996The 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 July 1996A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.