Daily Practice · Higher Plus
February 1967 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1967 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1967Work out the coordinates of the turning point of y = x^2 - 6x + 7.
- 2nd February 1967y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 4.
- 3rd February 1967The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 4th February 1967A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 5th February 1967On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th February 1967A 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.
- 7th February 1967Simplify (x^2 + 2x - 3)/(x + 3).
- 8th February 1967A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 9th February 1967In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 10th February 1967The probability of winning a game is 3/8. A player expects 24 wins. How many games did they play?
- 11th February 1967A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 12th February 1967x = 179 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th February 1967In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 7 in terms of an integer n?
- 14th February 1967y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 15th February 1967In a vector proof you find that vector PQ = 3a + 2b and vector RS = 9a + 6b. What does this show about PQ and RS?
- 16th February 1967A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 17th February 1967On 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?
- 18th February 1967A car covers 340 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th February 1967Make x the subject of 5x + 2 = y(x + 2).
- 20th February 1967y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 21st February 1967A cuboid measures 13 cm by 6 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd February 1967A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd February 1967A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 24th February 1967Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 25th February 1967Write 5/(x - 2) + 4/(x + 6) as a single fraction.
- 26th February 1967y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 64.
- 27th February 1967A cuboid measures 5 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th February 1967A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?