Daily Practice · Higher Plus
September 1978 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1978 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1978Use the iteration x(n+1) = cube root of (5x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 2nd September 1978A train slows steadily from 38 m/s to rest in 8 seconds. Work out its deceleration.
- 3rd September 1978The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 4th September 1978A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 5th September 1978A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 6th September 1978A rectangle is 14 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th September 1978Work out the nth term of the quadratic sequence -1, -3, -3, -1, ...
- 8th September 1978y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 9th September 1978In 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.
- 10th September 1978The probability of winning a game is 3/5. A player expects 12 wins. How many games did they play?
- 11th September 1978On 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?
- 12th September 1978Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 13th September 1978The point (-5, -4) lies on y = f(x). Write down its image on y = -f(x).
- 14th September 1978y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 15th September 1978In a vector proof you find that vector PQ = a + b and vector RS = 2a + 2b. What does this show about PQ and RS?
- 16th September 1978A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 17th September 1978A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 18th September 1978A block has mass 310 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th September 1978Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 20th September 1978y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 36.
- 21st September 1978A cuboid measures 9 cm by 9 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd September 1978A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd September 1978On 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?
- 24th September 1978x = 93 and y = 75, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th September 1978f(x) = 6x - 2 and g(x) = 5x - 8. Work out fg(3).
- 26th September 1978A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.
- 27th September 1978A cuboid measures 13 cm by 8 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th September 1978A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th September 1978A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 30th September 1978A car covers 430 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.