Daily Practice · Higher Plus
July 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1990A train slows steadily from 28 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd July 1990The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 3rd July 1990A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 4th July 1990A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 5th July 1990Simplify sqrt(50) + sqrt(32), giving your answer in the form a sqrt(b).
- 6th July 1990Solve x^2 - 10x + 16 < 0.
- 7th July 1990y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 8th July 1990In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 9th July 1990The probability of winning a game is 3/4. A player expects 9 wins. How many games did they play?
- 10th July 1990On 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?
- 11th July 1990A rectangle is 18 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th July 1990Write x^2 - 6x + 15 in the form (x + a)^2 + b.
- 13th July 1990y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 14th July 1990In a vector proof you find that vector PQ = 2a - 4b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 15th July 1990A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 16th July 1990A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 17th July 1990Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 18th July 1990Work out the coordinates of the turning point of y = x^2 - 16x - 1.
- 19th July 1990y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 64.
- 20th July 1990A cuboid measures 10 cm by 14 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st July 1990A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd July 1990On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd July 1990A block has mass 430 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th July 1990Simplify (x^2 - 8x + 15)/(x - 3).
- 25th July 1990A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 26th July 1990A cuboid measures 7 cm by 6 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th July 1990A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th July 1990A 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?
- 29th July 1990x = 108 and y = 70, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th July 1990In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 31st July 1990y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.