Daily Practice · Higher Plus
December 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1957x = 188 and y = 146, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd December 1957Make x the subject of 5x + 4 = y(x + 4).
- 3rd December 1957y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 4th December 1957In a vector proof you find that vector PQ = 6a + 3b and vector RS = 18a + 9b. What does this show about PQ and RS?
- 5th December 1957A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 6th December 1957On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th December 1957A car covers 500 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th December 1957Write 2/(x + 4) + 2/(x - 4) as a single fraction.
- 9th December 1957y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 10th December 1957A cuboid measures 5 cm by 11 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th December 1957A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th December 1957A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 13th December 1957Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 14th December 1957Solve 8x^2 + 6x + 1 = 0.
- 15th December 1957y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 36.
- 16th December 1957A cuboid measures 11 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th December 1957A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th December 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th December 1957Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
- 20th December 1957f(x) = 4x + 12. Work out the inverse function f^-1(x).
- 21st December 1957A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd December 1957The 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.
- 23rd December 1957A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 24th December 1957A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 25th December 1957A rectangle is 22 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th December 1957Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 27th December 1957y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 28th December 1957In 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.
- 29th December 1957The probability of winning a game is 1/5. A player expects 18 wins. How many games did they play?
- 30th December 1957On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st December 1957Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).