Daily Practice · Higher Plus
September 1968 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1968 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1968In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 2nd September 1968The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
- 3rd September 1968On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th September 1968A rectangle is 17 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th September 1968f(x) = 6x - 2 and g(x) = 3x + 8. Work out fg(4).
- 6th September 1968A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 7th September 1968In a vector proof you find that vector PQ = 5a + b and vector RS = 20a + 4b. What does this show about PQ and RS?
- 8th September 1968A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 9th September 1968A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 10th September 1968Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 11th September 1968The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 12th September 1968y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 13th September 1968A cuboid measures 14 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th September 1968A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th September 1968On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th September 1968A block has mass 400 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.
- 17th September 1968A quadratic sequence starts 17, 35, 61, 95. Work out the second difference, and the coefficient of n^2.
- 18th September 1968y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 19th September 1968A cuboid measures 9 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th September 1968A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st September 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 22nd September 1968x = 38 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd September 1968Solve x^2 + 10x + 16 < 0.
- 24th September 1968y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 9.
- 25th September 1968The 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.
- 26th September 1968A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 27th September 1968On 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?
- 28th September 1968A car covers 370 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th September 1968Write x^2 - 4x + 8 in the form (x + a)^2 + b.
- 30th September 1968A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.