Daily Practice · Higher Plus
October 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1990A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 2nd October 1990On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd October 1990A rectangle is 23 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th October 1990The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 5th October 1990A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 6th October 1990In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 7th October 1990The probability of winning a game is 1/8. A player expects 12 wins. How many games did they play?
- 8th October 1990A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 9th October 1990Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 10th October 1990A quadratic sequence starts 7, 22, 43, 70. Work out the second difference, and the coefficient of n^2.
- 11th October 1990y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 12th October 1990In a vector proof you find that vector PQ = 4a - 5b and vector RS = 12a - 15b. What does this show about PQ and RS?
- 13th October 1990A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 14th October 1990On 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?
- 15th October 1990A block has mass 750 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th October 1990Solve x^2 + 9x + 8 < 0.
- 17th October 1990y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 18th October 1990A cuboid measures 15 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th October 1990A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th October 1990A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 21st October 1990x = 116 and y = 96, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd October 1990Write x^2 + 14x - 4 in the form (x + a)^2 + b.
- 23rd October 1990y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 25.
- 24th October 1990A cuboid measures 4 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th October 1990A bag holds 6 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th October 1990On 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?
- 27th October 1990A car covers 200 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 October 1990Work out the coordinates of the turning point of y = x^2 - 8x + 3.
- 29th October 1990A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 30th October 1990The 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 October 1990A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.