Daily Practice · Higher Plus
December 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1958 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1958On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd December 1958Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 3rd December 1958The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 4th December 1958y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 5th December 1958A cuboid measures 10 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th December 1958A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th December 1958A 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?
- 8th December 1958A block has mass 860 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th December 1958A quadratic sequence starts 9, 26, 53, 90. Work out the second difference, and the coefficient of n^2.
- 10th December 1958y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 11th December 1958A cuboid measures 11 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th December 1958A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th December 1958On 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?
- 14th December 1958x = 36 and y = 21, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th December 1958Solve x^2 + 5x + 6 < 0.
- 16th December 1958A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 17th December 1958The 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.
- 18th December 1958A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 19th December 1958A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 20th December 1958A car covers 640 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.
- 21st December 1958Write x^2 + 12x - 7 in the form (x + a)^2 + b.
- 22nd December 1958y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 23rd December 1958In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 24th December 1958The probability of winning a game is 4/5. A player expects 32 wins. How many games did they play?
- 25th December 1958On 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?
- 26th December 1958Rationalise the denominator of 66/sqrt(6), giving your answer in its simplest form.
- 27th December 1958Work out the coordinates of the turning point of y = x^2 + 10x + 8.
- 28th December 1958y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 29th December 1958In a vector proof you find that vector PQ = a - 2b and vector RS = 3a - 6b. What does this show about PQ and RS?
- 30th December 1958A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 31st December 1958A 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?