Daily Practice · Higher Plus
December 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1959 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1959A 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?
- 2nd December 1959A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 3rd December 1959Simplify sqrt(12) + sqrt(12), giving your answer in the form a sqrt(b).
- 4th December 1959f(x) = 4x + 5. Work out the inverse function f^-1(x).
- 5th December 1959y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 36.
- 6th December 1959A cuboid measures 14 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th December 1959A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th December 1959On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th December 1959A rectangle is 16 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th December 1959Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 11th December 1959A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 12th December 1959The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 13th December 1959A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 14th December 1959A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 15th December 1959Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 16th December 1959Use the iteration x(n+1) = cube root of (10x(n) + 8) with x(0) = 4. Work out x(1) to 3 decimal places.
- 17th December 1959y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 18th December 1959In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 19th December 1959The probability of winning a game is 3/5. A player expects 66 wins. How many games did they play?
- 20th December 1959On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st December 1959A block has mass 270 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.
- 22nd December 1959Work out the nth term of the quadratic sequence -5, -7, -7, -5, ...
- 23rd December 1959y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 24th December 1959In a vector proof you find that vector PQ = 5a + 3b and vector RS = 20a + 12b. What does this show about PQ and RS?
- 25th December 1959A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 26th December 1959A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 27th December 1959x = 90 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th December 1959The point (-4, 2) lies on y = f(x). Write down its image on y = f(x - 2).
- 29th December 1959y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 16.
- 30th December 1959A cuboid measures 10 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st December 1959A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?