Daily Practice · Higher Plus
November 1975 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1975 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1975A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 2nd November 1975On 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?
- 3rd November 1975A block has mass 880 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.
- 4th November 1975f(x) = 2x + 6. Work out the inverse function f^-1(x).
- 5th November 1975A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 6th November 1975A cuboid measures 6 cm by 9 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th November 1975A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th November 1975A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 9th November 1975x = 86 and y = 37, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th November 1975Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 11th November 1975y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 12th November 1975A cuboid measures 10 cm by 10 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th November 1975A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th November 1975On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th November 1975A car covers 130 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th November 1975Use the iteration x(n+1) = cube root of (3x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 17th November 1975y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 18th November 1975The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 19th November 1975A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 20th November 1975A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 21st November 1975Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 22nd November 1975Work out the nth term of the quadratic sequence -3, 1, 11, 27, ...
- 23rd November 1975y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 64.
- 24th November 1975In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 25th November 1975The probability of winning a game is 3/4. A player expects 30 wins. How many games did they play?
- 26th November 1975On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th November 1975Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 28th November 1975The point (5, 0) lies on y = f(x). Write down its image on y = f(x - 6).
- 29th November 1975A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 30th November 1975In a vector proof you find that vector PQ = a - 2b and vector RS = 3a - 6b. What does this show about PQ and RS?