Daily Practice · Higher Plus
January 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1959 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1959Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 2nd January 1959Simplify (x^2 - 8x + 7)/(x - 7).
- 3rd January 1959y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 49.
- 4th January 1959A cuboid measures 10 cm by 13 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th January 1959A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th January 1959On 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?
- 7th January 1959A rectangle is 4 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th January 1959In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 9th January 1959A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 10th January 1959A cuboid measures 7 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th January 1959A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th January 1959A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 13th January 1959Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 14th January 1959Make x the subject of 2x + 5 = y(x + 5).
- 15th January 1959y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 16th January 1959The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 17th January 1959A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 18th January 1959On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th January 1959A block has mass 670 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th January 1959Write 2/(x + 3) + 5/(x - 1) as a single fraction.
- 21st January 1959y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 22nd January 1959In 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.
- 23rd January 1959The probability of winning a game is 3/4. A player expects 42 wins. How many games did they play?
- 24th January 1959A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 25th January 1959x = 66 and y = 37, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th January 1959Solve 6x^2 + 23x + 20 = 0.
- 27th January 1959y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 16.
- 28th January 1959In a vector proof you find that vector PQ = 5a - 3b and vector RS = 20a - 12b. What does this show about PQ and RS?
- 29th January 1959A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 30th January 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?
- 31st January 1959A car covers 650 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.